Questions: A plane flies northwest out of O'Hare Airport in Chicago at a speed of 400 km / hr in a direction of 150 degrees (i.e., 30 degrees north of west). The Canadian border is located a distance of 1500 km due north of Chicago. The plane will cross into Canada after approximately hours. a. 0.13 b. 0.23 c. 0.27 d. 3.75 e. 4.33 f. 6.49 g. 7.50 h. None of these are even close.

Solution Steps

The plane is flying at a speed of \(400 \, \text{km/hr}\) in a direction of 150 degrees, which is 30 degrees north of west. To find the northward component of the velocity, we use the cosine of the angle:

\[ v_{\text{north}} = 400 \times \cos(30^\circ) \]

Using the value \(\cos(30^\circ) = \frac{\sqrt{3}}{2} \approx 0.8660\), we calculate:

\[ v_{\text{north}} = 400 \times 0.8660 = 346.4 \, \text{km/hr} \]

The Canadian border is 1500 km due north of Chicago. To find the time it takes for the plane to reach the border, we use the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Velocity}} \]

Substituting the known values:

\[ \text{Time} = \frac{1500}{346.4} \approx 4.33 \, \text{hours} \]

Final Answer